ca. Feb. 3, 1776

Table of ratios of Velocities of Shot issuing from different Lengths of cannon charged with different quantities of powder.

Velocities of a Ball in a Second of time when the canon are of the Length of as the diameters below express

Parts of the Weight of Shot in powder	12	15	18	21	24	27	30	36 Diam.
powder 1/4 or 2 1/4 lb. ration for 9 lbr.	1043	1052	1058	1063	1066	1068	1071	1074
do. 1/3 or 3 lb. do	1186	1200	1210	1217	1224	1224	1229	1234
do. 1/2 or 4 1/2 lb. do.	1406	1434	1452	1465	1475	1482	1488	1497
do. 2/3 or 6 lb.	1586	1613	1641	1662	1677	1688	1698	1711

151all the remarks that can be made upon this table, are of the utmost importance to the caster of cannon.

1st, when the charge is 1/4 of the weight of the Shot, a difference arises between the Velocities of Shot,

in cannon of 12 to 15 diameters of 9 ft. per Secd:

in do. from 15 to 18 do. it is 6

in do. from 18 to 21 do. it is 5

in do. from 21 to 24 do. it is 3

in do. from 24 to 27 do. only 2

in do. from 27 to 30 do. again 3

in do. from 30 to 36 do. Still 3

Ergo the difference between the Velocity of Shot increases no more between 15 & 36 Diameters Length than 22 ft. in one Second of time therefore when the piece has a Light charge of 1/4 the weight of its caliber the Length from 12 to 15 feet diameters1 is best.

Again when charged with 1/3 weight of the Shot when the piece is of 12 to 15 Diameters in Length the increase of velocity is more than between any other Lengths in the table, therefore from 12 to 15 Calibers is the preferable Length.

Thirdly when the charge is 1/2 the weight, the velocity increases equally between 15 & 18 as between 12 & 15 diameters & from 18 to 36 it still decreases, therefore it seems indifferent whether the Gun be from 12 to 15 or 15 to 18 diameters Long But 12 or 15 taking Less metal than from 15 to 18 it again appears that from 12 to 15 is the best Length.

Lastly when we use 2/3 of the weight it appears that from 12 to 21 Diameters is indifferent. But by the same reasoning as before why should we Lengthen a piece to near double its weight when we see that from 12 to 15 is as good as from 15 to 18 & that from thence it decreases in velocity therefore 12 to 15 diams: again appears best.

But we see the velocity again encreasing from 27 to 36 diams. therefore 40 or 50 Diameters might be still better but why encrease the quantity of Metal in so extravagant a ratio when a small quantity so effectually serves us.

I copied this table from a Book where it stood copied from Mullers artillery 2 (an author I never had an opportunity to see) there were also some remarks said to be quoted from the same Book, But though they tend to prove the same as I have here demonstrated, yet they were crude, inconclusive & even absurd, I therefore suspected the transcribers care or fidelity & therefore ventured to state them as above written.

152

I have examined most of the field pieces in our possession especially Brass 6 prs: & find them all to be under 15 diameters

B: Romans Engineer

Brass feild peices at Philada.3
Caliber 3 inch 6/10	wt. 5-0-3}
another	wt. 4-3-14 }	length 4 feet 7

Shot	Caliber	inch
4 lb	3 in. 1/20		3.05
6 -	3 --		3,49
9 -	4 --		4
18 -	---		5.,04
24 --			5.,60
32 --			6.,37
42 --			6.,51

Diameters of the shotts & Calibers of the Guns; taken from Muller’s Artillery see facing page.

RC ; endorsed, not in RTP’s hand.

1.

Corrected in another hand.

2.

John Muller, A Treatise of Artillery . . . To Which is Prefixed, A Theory of Powder Applied to Fire-Arms. For the Use of the Royal Academy of Artillery (London, 1757, and later editions).

3.

From this line onwards in RTP’s hand.